Ducks know game theory?

Game theory sounds like something only intellectuals would use. After all, technical math is required for academic courses. And many introductory problems border on the bizarre, like learning how to solve a game of “hot or not.” Game theory is famously associated with the RAND institute, a think tank of intellectuals solving abnormal problems like nuclear warfare.

So it’s surprising that years of research have indicated the opposite trend: game theory is useful for everyone even in routine problems. Game theory doesn’t require a formal education. In fact, game theory doesn’t require any education at all. This point is vividly demonstrated in an experiment concerning ducks, game theory, and foraging food.

Tom Siegfried narrates the experiment in his book A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature.

Siegfried’s explanation is so good that I will not try to improve upon it. I can’t reprint it here due to copyright restrictions, but I can do something almost as good.

I direct you to the full-text on the National Academies Press website. The duck experiment is explained in the following three pages. Please follow the links for pages 73-75 to read the text.

Page 73: (Image or html)

Page 74: (Image or html)

Page 75: (Image or html)

If you liked that explanation, I think you’ll like the entire book. The book goes through how game theory has been used in a wide-range of scientific research. It is a very pleasant read.

Amazingly, you can read the whole thing for free at the NAP website.

(If you prefer a hard copy, get it from your library, or from Amazon.)



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  • http://bizop.ca michael webster

    The use of game theory as an optimizing device, as opposed to rational calculation, may turn out to be very important.

    In an optimizing theory, there is no overt appeal to rationality – the agents are not assumed to be even thinking. The self gene theory is an optimizing theory, but confusingly overlaid with decision making metaphors.

    In a rational choice theory, we are, on the other hand, trying to understand the mechanics of decision making by reflective agents.

    The duck example is interesting because it may shed light on why individuals engage in probability matching, the tendency to pick between two outcomes based on their relative frequency instead of picking simply the more frequent outcome. Some argue that the probability matching makes sense when you are in a competition for food, energy, etc, and lab experiments which show the apparent irrationality of probability matching are overlooking this fact.
    (Nice reference to the NAP site.)

  • http://www.mawsoft.com/blog RohoMech

    So, I wonder if the ducks just have some iterative sorting algorithm / heuristic that would lead to a Nash equilibrium.

  • http://www.mindyourdecisions.com/blog/ Presh Talwalkar

    Michael Webster:
    Great point. The biology applications are relatively new to me and this distinction between rational choice theory and optimizing theory is interesting. The duck example also reminded me of how tennis players end up having a random distribution on serves.

    RohoMech:
    Perhaps ducks are hard-wired with some algorithm. That’s what the author suggests–that game theory predicts correctly since it tells us something deeper about nature.

  • http://www.mawsoft.com/blog RohoMech

    Presh

    Ah, I see your point. Hmm, so if I may pose a question, what might that algorithm be?

  • Tomas

    Game theory looks for equilibria. These can be achieved through introspection, learning or evolution. All of them result in the stabilization of choice distributions. Evolution is not even connected with conscious analysis but can result in a game-theoretic equilibrium. I think that ducks probably didn’t compute the solution but I think one should give them a little credit and accept that they are probably able to learn (although I think that training a duck would pose a big time challenge).
    I believe that the utility function of these ducks is not so hard to figure out – they want to eat as much as possible. Mental processes of humans would be probably more complicated by this experiment, something like: “I have to look like a total idiot swimming in the lake and chasing pieces of bread.” So it is difficult to predict what the humans would actually do. It seems to be the case that game theory is sometimes better suited for predicting the behavior of ducks than the behavior of people :)

  • http://bizop.ca michael webster

    Here is the basic idea.

    Suppose E happens with probability P and F happens with probability Q, P + Q = 1.

    The rewards associated with E and F are the same.

    What rule of choice maximizes return? That is, how should you choose between E and F?

    It seems clear that choosing the event with higher probability is correct.

    But humans, rats, ducks and other animals appear to use the sub-optimal rule “probability matching.” That is, they choose E P times, and F Q times.

    While this may be irrational for one person decision makers, it may be rational for action within a group.

    Suppose E and F were different locations with food. Then if all the animals foraged at E all the time, the competition might not be worth the fight – thus the rational choice from an individual’s perspective given an understanding of what the group might do may make matching probability an optimal rule.

  • http://www.mindyourdecisions.com/blog/ Presh Talwalkar

    Tomas:
    Well said–game theory seems to work since ducks have a predictable response, namely, going for more food.

    Michael Webster:
    This is very interesting, the concept of probability matching. I have to read up on more beyond the sports applications I know about.

  • Gary Asselbergs

    The rule in duck land is you’re supposed to quack when feeding. It is considered good table manners. It’s great, a good quack during dinner is hilarious, and if you’re a hungry duck, then all have to do is home into the quacks and dig it.

    This is fine when an abundance of food is available. But what happens during a famine?

    I mean if you where a duck and found some food, wouldn’t you be better off being silent, gorge yourself, listen carefully for any quacks, and then fly off to get your fair share?

    I’ve never meet a silent duck on our lake, they all seem to quack. So how do they do it?

  • Tomas

    @Gary: Here is how I see it.

    It is a big world for a little duck and so the ducks must stick together to survive. Let`s say that the probability of finding the food is equal for all ducks, but some ducks have more luck one day and some on the other day. Sharing the food doesn’t change the total income of food of one duck but it changes the way how food is devided in time. Let’s suppose there are 10 ducks in a flock and each finds food of quantity 1 with the probability of 5%. If the ducks eat only their own food, they eat 1 food every 20th day. If they share the food, they eat every day on average one 20th of the whole portion. If one 20th is enough for a comfortable living, it is for sure better than the other alternative. It is even better in case a duck cannot last 20 days without eating something.

    Of course in the case of a famine the situation is different. The probability of finding food would be much lower. If it is so low that the portion of food a duck gets when sharing is not sufficient to survive a longer period than the period between eating the whole portion and dying, quacking doesn´t make sense anymore. So in the case of a famine the uncertainty about the future makes the duck-dinner into a one-shot game and the manners of ducks probably change.

    So according to these computations it is better to signal the presence of the food from a long-term perspective because then the duck can expect the others to do so as well. If a duck-dinner was a oneshot game as in the case of a famine, it would be rational to betray the flock and not to quack. But an empirical evidence through experiment would be too cruel, so we may never uncover the true nature of ducks’ character. ;)

  • http://www.mindyourdecisions.com/blog/ Presh Talwalkar

    Gary Asselbergs:
    Didn’t realize that ducks have dining etiquette ;)

    Tomas responded with an interesting take that ducks signal out of group cooperation. Sounds convincing but I would be interested in reading more. It does make sense that repeated group interaction would produce cooperation.

  • Tomas Kubis

    @Presh – literature on cooperative behavior

    I would paradoxically recommend a book that I did not have opportunity to read so far. Not that I would not want to. It is The evolution of cooperation by Robert Axelrod (or the article from Science with the same name by Axelrod and Hamilton). It is an older work but based on the reviews, it is supposed to be an interesting reading with interesting conclusions.

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